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A246892 T(n,k)=Number of length n+4 0..k arrays with some pair in every consecutive five terms totalling exactly k.

%I A246892 #6 Jul 23 2025 11:32:37
%S A246892 30,231,58,900,673,112,2701,3364,1961,216,6210,12481,12544,5711,416,
%T A246892 12931,33294,57585,46656,16621,802,23400,79345,177648,264981,173056,
%U A246892 48393,1546,40281,159688,484297,942216,1216081,643204,140893,2980,63750
%N A246892 T(n,k)=Number of length n+4 0..k arrays with some pair in every consecutive five terms totalling exactly k.
%C A246892 Table starts
%C A246892 ....30.....231.......900.......2701........6210........12931........23400
%C A246892 ....58.....673......3364......12481.......33294........79345.......159688
%C A246892 ...112....1961.....12544......57585......177648.......484297......1079680
%C A246892 ...216....5711.....46656.....264981......942216......2934691......7216512
%C A246892 ...416...16621....173056....1216081.....4971120.....17677453.....47799488
%C A246892 ...802...48393....643204....5592169....26346486....107053441....319477960
%C A246892 ..1546..140893...2390116...25710385...139555230....647845357...2132283592
%C A246892 ..2980..410197...8880400..118192273...738947844...3918872917..14219886016
%C A246892 ..5744.1194243..32993536..543322645..3912529200..23704560247..94826520320
%C A246892 .11072.3476929.122589184.2497751105.20719113168.143411404177.632600369216
%H A246892 R. H. Hardin, <a href="/A246892/b246892.txt">Table of n, a(n) for n = 1..1835</a>
%F A246892 Empirical for column k:
%F A246892 k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4)
%F A246892 k=2: [order 14]
%F A246892 k=3: [order 10]
%F A246892 k=4: [order 31]
%F A246892 k=5: [order 14]
%F A246892 k=6: [order 39]
%F A246892 k=7: [order 15]
%F A246892 k=8: [order 40]
%F A246892 k=9: [order 15]
%F A246892 Empirical for row n:
%F A246892 n=1: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)
%F A246892 n=2: [order 10]
%F A246892 n=3: [order 12]
%F A246892 n=4: [order 13]
%F A246892 n=5: [order 14]
%F A246892 n=6: [order 16]
%F A246892 n=7: [order 18]
%e A246892 Some solutions for n=3 k=4
%e A246892 ..0....0....2....0....2....3....4....3....1....2....3....1....4....4....3....4
%e A246892 ..3....4....0....1....3....0....2....2....1....0....3....1....1....1....0....1
%e A246892 ..0....0....1....0....4....0....1....3....1....3....0....2....3....0....4....4
%e A246892 ..2....4....2....3....0....4....3....4....2....0....1....4....0....2....2....3
%e A246892 ..1....1....0....1....1....4....1....2....3....2....2....3....2....2....1....1
%e A246892 ..4....0....2....1....1....4....2....1....1....4....2....2....1....2....0....2
%e A246892 ..4....1....2....2....4....3....0....3....2....1....3....4....3....1....2....2
%Y A246892 Column 1 is A135492(n+4)
%K A246892 nonn,tabl
%O A246892 1,1
%A A246892 _R. H. Hardin_, Sep 06 2014